Year

Key Concepts (Statutory Requirements)

Year 1

Addition and Subtraction
 Read, write and interpret mathematical statements involving addition (+), subtraction () and equals (=) signs.
 Represent and use number bonds and related subtraction facts within 20
 Add and subtract onedigit and twodigit numbers to 20, including zero
 Solve one step problems that involve addition and subtraction, using concrete objects and pictures, and missing number problems such as 7 =  9
Multiplication and Division
 Solve onestep problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher.

Year 2

Addition and Subtraction
 solve problems with addition and subtraction:
 using concrete objects and pictorial representations, including those involving numbers, quantities and measures
 applying their increasing knowledge of mental and written methods
 recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100
 add and subtract numbers using concrete objects, pictorial representations, and mentally, including:
 a twodigit number and ones
 a twodigit number and tens
 two twodigit numbers
 adding three onedigit numbers
 show that addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot
 recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems.
Multiplication and Division
 recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers
 calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs
 show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot
 solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts.

Year 3

Addition and Subtraction
 add and subtract numbers mentally, including:
 a threedigit number and ones
 a threedigit number and tens
 a threedigit number and hundreds
 add and subtract numbers with up to three digits, using formal written methods of columnar addition and subtraction
 estimate the answer to a calculation and use inverse operations to check answers
 solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction.
Multiplication and Division
 recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables
 write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for twodigit numbers times onedigit numbers, using mental and progressing to formal written methods
 solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects.

Year 4

Addition and Subtraction
 add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate
 estimate and use inverse operations to check answers to a calculation
 solve addition and subtraction twostep problems in contexts, deciding which operations and methods to use and why.
Multiplication and Division
 recall multiplication and division facts for multiplication tables up to 12 × 12
 use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together three numbers
 recognise and use factor pairs and commutatively in mental calculations
 multiply twodigit and threedigit numbers by a onedigit number using formal written layout
 solve problems involving multiplying and adding, including using the distributive law to multiply two digit numbers by one digit, integer scaling problems and harder correspondence problem such as n objects are connected to m objects.

Year 5

Addition and Subtraction
 add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)
 add and subtract numbers mentally with increasingly large numbers
 use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy
 solve addition and subtraction multistep problems in contexts, deciding which operations and methods to use and why.
Multiplication and Division
 identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers
 know and use the vocabulary of prime numbers, prime factors and composite (nonprime) numbers
 establish whether a number up to 100 is prime and recall prime numbers up to 19
 multiply numbers up to 4 digits by a one or twodigit number using a formal written method, including long multiplication for twodigit numbers
 multiply and divide numbers mentally drawing upon known facts
 divide numbers up to 4 digits by a onedigit number using the formal written method of short division and interpret remainders appropriately for the context
 multiply and divide whole numbers and those involving decimals by 10, 100 and 1000

Year 6

Addition, Subtraction, Multiplication and Division
 multiply multidigit numbers up to 4 digits by a twodigit whole number using the formal written method of long multiplication
 divide numbers up to 4 digits by a twodigit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context
 divide numbers up to 4 digits by a twodigit number using the formal written method of short division where appropriate, interpreting remainders according to the context
 perform mental calculations, including with mixed operations and large numbers
 identify common factors, common multiples and prime numbers
 use their knowledge of the order of operations to carry out calculations involving the four operations
 solve addition and subtraction multistep problems in contexts, deciding which operations and methods to use and why
